Cut mesh with circle pie chart like mesh for animation
There's a lot of ways that you can change the shape of the cutting mesh.
For versions where you only alter the shape, you can animate whether the boolean even affects the cylinder , so you have a full cylinder to start with. You simply switch it on for the first frame of cutting.

You can use shape keys which is a very cool answer, you could use hooks, you could use an armature.

But why not go overboard with this and boolean Napoleon the boolean?

From Haunt's bag of tricks:

The yellow box is just ever so slightly larger than the orange one. When they align, it swallows the orange one whole in effect making it cease to exist...  sort of. 

If I rotate the yellow one, it reveals more and more of the orange box. I simply subtract the yellow box from the orange box and I subtract the result from the cylinder. The possibilities are endless.

Although this only works for a 180° cutaway.



TLDR: yellow eats orange, orange eats cylinder. YUM!